Non-perturbative effects of short-range spatial correlations at the two-particle level

TL;DR

This paper investigates how short-range correlations in two-dimensional systems cause the failure of self-consistent perturbation theory, revealing their role in the Mott transition and phase separation through advanced many-body calculations.

Contribution

It derives a consistent Bethe-Salpeter equation formalism at the CDMFT level and demonstrates how short-range correlations lead to vertex divergences before local DMFT predictions.

Findings

Vertex divergence occurs at lower interactions due to short-range antiferromagnetic fluctuations.

Sign change in charge susceptibility eigenvalues signals the Mott transition.

Short-range correlations significantly alter two-particle response functions.

Abstract

By means of cellular dynamical mean-field theory (CDMFT) we study how short-range correlations drive the breakdown of the self-consistent perturbation theory in two-dimensional systems and the most relevant physical consequences associated to it. To this aim, we first derive in a structured and consistent way the Bethe-Salpeter equation (BSE) formalism at the CDMFT level in all physical channels, explicitly addressing the important aspect of the related Ward identities. In this context, we perform systematic calculations of the BSE for the two-dimensional Hubbard model at half-filling at intermediate coupling. Our study illustrates how the divergence of a fundamental building block of the BSE in the charge channel, the two-particle irreducible vertex, systematically occurs at lower interactions than in the (purely local) DMFT case, due to short-range antiferromagnetic fluctuations. Further, the change of sign of the eigenvalues of the generalized charge susceptibility associated to the vertex divergences is identified as the essential prerequisite to drive, at larger interaction values, the physics of the Mott transition in two dimensions, as well as of the adjacent phase-separation instabilities.